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Quantum Computers

We always fear what we do not know. This statement has been proven right throughout the history of mankind and has resulted in significant evolution, even though there was always speculation of singularity (existential crisis).

Not hopping the "Quantum Computers will destroy Bitcoin" wagon; I'd like to explore the positive outcomes or the use cases that Quantum computers could be used for, in blockchain technology.

Edit 1:

Just to clarify, this is not a duplicate question as it discovers only positive impacts that quantum computing can bring to the technology.

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A couple very hypothetical examples:

  • Quantum channels: These channels allow wiretap resistant transmission of data. Bitcoin users can share secret information such as keys over quantum channels in such a way that any wiretapping would be detectable.
  • Database queries: Quantum computers can search through a database in time O(N^(1/3)). This could potentially speed up lookups in a blockchain. Say I want to transactions that correspond to my public key. For one billion transactions this can be done in only a thousand steps (ignoring gigantic constants probably).
  • Quantum simulation could perhaps lead to better hardware so that's always nice.

However, the biggest real impact that quantum computers have right now on cryptography and thus cryptocurrencies is something different: They encourage cryptographers to explore new and interesting schemes and cryptographic assumptions. The study of these new assumptions and schemes could lead to more useful cryptographic tools which we couldn't build from other assumptions. The prime example for this is fully homomorphic encryption which can be built from ideal lattices. These lattices were first used in cryptography to build quantum resistant cryptography.

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  • So in accordance with the answer, quantum powered encryption as well as quantum resistant ones are highly possible. Your last para seems quite intriguing and one that is coming from a person who knows cryptography. As every persons search engine work in accordance to their tailored customisations, I would take a while to reach the right resources to study ‘cryptography and quantum computing’. Could you be kind enough to direct me to a few resources for the same?
    – Junaid Shaikh
    Commented Jun 27, 2018 at 21:35
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    Yes quantum resistant cryptography exists and could be used today (it just is not as efficient as non-quantum resistant cryptography). As for resources, your best bet is probably graduate courses like this one (crypto.stanford.edu/cs355/18sp/syllabus). I can also highly recommend this book by Boneh and Shoup which is still being written: toc.cryptobook.us (disclaimer: I am biased). Chapter 14 and 16 will be the most relevant ones. If you really want to go into the weeds then you can find the cutting edge research at eprint.iacr.org
    – Benedikt Bünz
    Commented Jul 9, 2018 at 10:16

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